$g(n) = n^{2}-2n$ $h(n) = 2n^{2}-6n-4(g(n))$ $ h(g(5)) = {?} $
Answer: First, let's solve for the value of the inner function, $g(5)$ . Then we'll know what to plug into the outer function. $g(5) = 5^{2}+(-2)(5)$ $g(5) = 15$ Now we know that $g(5) = 15$ . Let's solve for $h(g(5))$ , which is $h(15)$ $h(15) = 2(15^{2})+(-6)(15)-4(g(15))$ To solve for the value of $h$ , we need to solve for the value of $g(15)$ $g(15) = 15^{2}+(-2)(15)$ $g(15) = 195$ That means $h(15) = 2(15^{2})+(-6)(15)+(-4)(195)$ $h(15) = -420$